Subgroups — #28476571

Order 15104.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₉₄₄	C₂	1	1	yes	maximal, characteristic
2	#21422296	C₂	1	1	yes	maximal, characteristic
3	C₂×C₅₉×C₆₄	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₄₇₂	—	2	1	no	—
5	Dic₉₄₄	—	2	1	no	—
6	Dic₉₄₄	C₄	1	2	yes	complemented
7	#16837228	—	2	1	no	—
8	C₂×C₃₂×C₅₉	C₂²	1	1	yes	characteristic
9	C₅₉×C₆₄	—	2	1	no	—
10	C₂×Dic₂₃₆	—	4	1	no	—
11	Dic₄₇₂	—	2	2	no	—
12	Dic₄₇₂	—	4	1	no	—
13	#14273661	—	4	1	no	—
14	C₂×C₁₆×C₅₉	D₄	1	1	yes	characteristic
15	C₃₂×C₅₉	C₂×C₄	1	1	yes	characteristic
16	C₃₂×C₅₉	D₄	1	1	yes	characteristic
17	C₂×Dic₁₁₈	—	8	1	no	—
18	C₂×C₈×C₅₉	D₈	1	1	yes	characteristic
19	C₄⋊Dic₅₉	—	8	1	no	—
20	Dic₂₃₆	—	4	2	no	—
21	Dic₂₃₆	—	8	1	no	—
22	C₁₆×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
23	C₁₆×C₅₉	SD₁₆	1	1	yes	characteristic
24	C₂×C₄×C₅₉	D₁₆	1	1	yes	characteristic
25	C₂×Dic₅₉	—	16	1	no	—
26	C₂×Dic₅₉	—	16	1	no	—
27	Dic₁₁₈	—	8	2	no	—
28	Dic₁₁₈	—	16	1	no	—
29	C₈×C₅₉	#102	1	1	yes	characteristic
30	C₈×C₅₉	SD₃₂	1	1	yes	characteristic
31	#7538	—	59	1	no	maximal, Sylow
32	C₂²×C₅₉	D₃₂	1	1	yes	characteristic
33	C₄×C₅₉	#357	1	1	yes	characteristic
34	C₄×C₅₉	SD₆₄	1	1	yes	characteristic
35	Dic₅₉	—	16	2	no	—
36	Dic₅₉	—	32	1	no	—
37	C₂×Q₆₄	—	59	1	no	—
38	C₂×C₆₄	D₅₉	1	1	yes	characteristic
39	#1423	—	59	1	no	—
40	C₂×C₅₉	#1415	1	1	yes	characteristic
41	C₂×C₅₉	SD₁₂₈	1	1	yes	characteristic
42	C₂×C₅₉	Q₁₂₈	1	1	yes	characteristic
43	C₂×Q₃₂	—	118	1	no	—
44	Q₆₄	—	59	2	no	—
45	Q₆₄	—	118	1	no	—
46	C₂×C₃₂	C₂×D₅₉	1	1	yes	characteristic
47	#366	—	118	1	no	—
48	C₆₄	—	2	1	no	—
49	C₅₉	#7538	1	1	yes	characteristic, complemented, Sylow
50	C₂×Q₁₆	—	236	1	no	—
51	Q₃₂	—	118	2	no	—
52	Q₃₂	—	236	1	no	—
53	C₂×C₁₆	D₂₃₆	1	1	yes	characteristic
54	#107	—	236	1	no	—
55	C₃₂	C₄×D₅₉	1	1	yes	characteristic
56	C₃₂	C₂²⋊D₅₉	1	1	yes	characteristic
57	C₂×Q₈	—	472	1	no	—
58	Q₁₆	—	472	1	no	—
59	Q₁₆	—	236	2	no	—
60	C₂×C₈	D₄₇₂	1	1	yes	characteristic
61	C₄⋊C₄	—	472	1	no	—
62	C₁₆	#11745660	1	1	yes	characteristic
63	C₁₆	(C₂×D₅₉)⋊C₄	1	1	yes	characteristic
64	Q₈	—	944	1	no	—
65	Q₈	—	472	2	no	—
66	C₂×C₄	—	944	1	no	—
67	C₂×C₄	—	944	1	no	—
68	C₂×C₄	D₉₄₄	1	1	yes	characteristic
69	C₈	#14273649	1	1	yes	characteristic
70	C₈	#14273672	1	1	yes	characteristic
71	C₂²	D₁₈₈₈	1	1	yes	characteristic
72	C₄	—	1888	1	no	—
73	C₄	—	944	2	no	—
74	C₄	#16837204	1	1	yes	characteristic
75	C₄	#16837241	1	1	yes	characteristic
76	C₂	#21422275	1	1	yes	characteristic
77	C₂	#21422312	1	1	yes	characteristic
78	C₂	Dic₁₈₈₈	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₁₈₈₈
commutator	C₃₂×C₅₉	C₂×C₄
Frattini	C₂×C₃₂	C₂×D₅₉
Fitting	C₂×C₅₉×C₆₄	C₂
socle, prime radical	C₂²×C₅₉	D₃₂
cosocle	C₂×C₃₂×C₅₉	C₂²
hypercenter	C₂×C₆₄	D₅₉
hypocenter	C₅₉	#7538
LCS	G ▷ C₃₂×C₅₉ ▷ C₁₆×C₅₉ ▷ C₈×C₅₉ ▷ C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×C₃₂ ◁ C₂×C₆₄

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
6. Dic₉₄₄	C₄	semidirect
49. C₅₉	#7538	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×Dic₉₄₄	2
#21422296	2
C₂×C₅₉×C₆₄	2
#7538	59